Finite Group Databasebeta

← #14642973

Subgroups — #14642973

Order 2816.

350 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076604C211yesmaximal, characteristic
2#13070173C211yesmaximal, characteristic
3#13070093C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic
5#13066438C211yesmaximal, characteristic
6#13066438C211yesmaximal, characteristic
7C11×#2072C211yesmaximal, characteristic
8C2×C11×#103—21no—
9C11×#391C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622843—21no—
12#10622599—21no—
13C2×#66872—21no—
14#10622541C2211yescharacteristic
15#10622541C2211yescharacteristic
16#10622274—21no—
17#10622274—21no—
18#10622268—21no—
19#10622268—21no—
20C11×#340—21no—
21C11×#336C2211yescharacteristic
22#10622167—21no—
23#10622167—21no—
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×C8×C11—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11—21no—
43C22×C11⋊C8—21no—
44C22×C11⋊C8—21no—
45C11×#103—42no—
46C11×#95—21no—
47C11×#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55#66872—42no—
56#7813—111nomaximal, Sylow
57C2×Q8×C11—21no—
58C2×Q8×C11—41no—
59C2×Q8×C11—41no—
60C2×Q8×C11SD1612yes—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C42×C11—41no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—81no—
88C4⋊Dic11—81no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93C4×Dic11—81no—
94C2×C11⋊C8—22no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100#2809—111no—
101#2099—111no—
102#2084—111no—
103#2072D1111yescharacteristic
104#1272—111no—
105#1271—111no—
106#1271—111no—
107C23×C11#12011yescharacteristic
108Q8×C11—42no—
109Q8×C11—81no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11C2×SD1611yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C8×C11—81no—
144C11⋊C8—42no—
145C11⋊C8—81no—
146C2×#106—221no—
147C2×#103—21no—
148#400—221no—
149#398—221no—
150#398—221no—
151#391—221no—
152#391C2×D1111yescharacteristic
153#389—111no—
154#389—111no—
155#387—221no—
156#387—221no—
157#384C2×D1111yescharacteristic
158#340—21no—
159#340—221no—
160#340—221no—
161#340—221no—
162#336—111no—
163#336—111no—
164#336C2×D1111yescharacteristic
165C22×C11#44811yescharacteristic
166C22×C11#44911yescharacteristic
167C22×C11#45211yescharacteristic
168C22×C11#45411yescharacteristic
169C22×C11#45511yescharacteristic
170C22×C11#45611yescharacteristic
171C22×C11#45811yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—42no—
179C4×C11—81no—
180C4×C11—161no—
181Dic11—81no—
182Dic11—81no—
183Dic11—81no—
184Dic11—81no—
185C22×Q8C22⋊D1111yescharacteristic
186C22×C8—21no—
187C22×C8—221no—
188C22×C8—221no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—111no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4C22⋊D1111yescharacteristic
201C2×C42—221no—
202C2×C42C22×D1111yescharacteristic
203#106—442no—
204#103—42no—
205#95—21no—
206#95—21no—
207#95—221no—
208#95—221no—
209#95—221no—
210#95—221no—
211#95—221no—
212#95—221no—
213#95—221no—
214C2×C11#160811yescharacteristic
215C2×C11#160911yescharacteristic
216C2×C11#161511yescharacteristic
217C2×C11#162611yescharacteristic
218C2×C11#164611yescharacteristic
219C2×C11#165311yescharacteristic
220C2×C11#166411yescharacteristic
221C2×Q8—21no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8#432412yes—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—41no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4—221no—
231C22×C4—221no—
232C22×C4D4×D1111yescharacteristic
233C22×C4D4×D1111yescharacteristic
234C22×C4C2×C22⋊D1111yescharacteristic
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—222no—
239C2×C8—441no—
240C2×C8—441no—
241C2×C8—441no—
242C2×C8—441no—
243C2×C8—441no—
244C4⋊C4—41no—
245C4⋊C4—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—881no—
261C4⋊C4—881no—
262C42—41no—
263C42—881no—
264C11#781311yescharacteristic, complemented, Sylow
265C23#6699011yescharacteristic
266Q8—42no—
267Q8—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4#6696711yescharacteristic
296C2×C4#6696911yescharacteristic
297C2×C4#6697111yescharacteristic
298C2×C4#6697211yescharacteristic
299C2×C4C2×#432411yescharacteristic
300C2×C4#6700411yescharacteristic
301C8—81no—
302C8—442no—
303C8—881no—
304C22#1062265311yescharacteristic
305C22#1062266611yescharacteristic
306C22#1062267411yescharacteristic
307C22#1062278511yescharacteristic
308C22#1062280011yescharacteristic
309C22#1062281411yescharacteristic
310C22#1062281811yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—81no—
319C4—161no—
320C4—881no—
321C4—881no—
322C4—881no—
323C4—881no—
324C2#1306760611yescharacteristic
325C2#1306761211yescharacteristic
326C2#1306764611yescharacteristic
327C2#1306771111yescharacteristic
328C2#1306784111yescharacteristic
329C2#1306789111yescharacteristic
330C2#1306794911yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2072C2
socle, prime radicalC23×C11#120
hypercenter#2072D11
hypocenterC11#7813
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
264. C11#7813semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130766042
#130701732
#130700932
#130664422
#130664382
C11×#20722
#781311